Finite Group Databasebeta

← Group #13048752

Character table — Group #13048752

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1222266912121212121818181827275454122226691212121212181818182727545412222669121212121218181818272754541222266912121212121818181827275454
order1333333233333666622664121212121212412121212121212121244121226666662666666666226641212121212124121212121212121212441212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-111111111111111111-1-1-1-111111111111111111-1-1-1-111111111111111111-1-1-1-1
χ31111111-111111-1-1-1-11-11-11111111-111111-1-1-1-11-11-11111111-111111-1-1-1-11-11-11111111-111111-1-1-1-11-11-1
χ41111111-111111-1-1-1-1-11-111111111-111111-1-1-1-1-11-111111111-111111-1-1-1-1-11-111111111-111111-1-1-1-1-11-11
χ5222222-102-1-1-1-10000020-1222222-102-1-1-1-10000020-1222222-102-1-1-1-10000020-1222222-102-1-1-1-10000020-1
χ6222222-102-1-1-1-100000-201222222-102-1-1-1-100000-201222222-102-1-1-1-100000-201222222-102-1-1-1-100000-201
χ722222-120-12-1-1-1000020-1022222-120-12-1-1-1000020-1022222-120-12-1-1-1000020-1022222-120-12-1-1-1000020-10
χ822222-120-12-1-1-10000-201022222-120-12-1-1-10000-201022222-120-12-1-1-10000-201022222-120-12-1-1-10000-2010
χ922-1-1-1222-1-12-1-12-1-1-1000022-1-1-1222-1-12-1-12-1-1-1000022-1-1-1222-1-12-1-12-1-1-1000022-1-1-1222-1-12-1-12-1-1-10000
χ1022-1-1-122-2-1-12-1-1-2111000022-1-1-122-2-1-12-1-1-2111000022-1-1-122-2-1-12-1-1-2111000022-1-1-122-2-1-12-1-1-21110000
χ1144444-2-20-2-21110000000044444-2-20-2-21110000000044444-2-20-2-21110000000044444-2-20-2-211100000000
χ1244-2-2-24-20-21-2110000000044-2-2-24-20-21-2110000000044-2-2-24-20-21-2110000000044-2-2-24-20-21-21100000000
χ1344-2-2-2-2401-2-2110000000044-2-2-2-2401-2-2110000000044-2-2-2-2401-2-2110000000044-2-2-2-2401-2-21100000000
χ1444-2-2-2-2-20111−1+3i32−1−3i320000000044-2-2-2-2-20111−1+3i32−1−3i320000000044-2-2-2-2-20111−1+3i32−1−3i320000000044-2-2-2-2-20111−1+3i32−1−3i3200000000
χ1544-2-2-2-2-20111−1−3i32−1+3i320000000044-2-2-2-2-20111−1−3i32−1+3i320000000044-2-2-2-2-20111−1−3i32−1+3i320000000044-2-2-2-2-20111−1−3i32−1+3i3200000000
χ166-36-3-300200000-12-1-100006-36-3-300200000-12-1-100006-36-3-300200000-12-1-100006-36-3-300200000-12-1-10000
χ176-36-3-300-2000001-21100006-36-3-300-2000001-21100006-36-3-300-2000001-21100006-36-3-300-2000001-2110000
χ186-3-36-300200000-1-12-100006-3-36-300200000-1-12-100006-3-36-300200000-1-12-100006-3-36-300200000-1-12-10000
χ196-3-36-300-20000011-2100006-3-36-300-20000011-2100006-3-36-300-20000011-2100006-3-36-300-20000011-210000
χ206-3-3-3600200000-1-1-1200006-3-3-3600200000-1-1-1200006-3-3-3600200000-1-1-1200006-3-3-3600200000-1-1-120000
χ216-3-3-3600-200000111-200006-3-3-3600-200000111-200006-3-3-3600-200000111-200006-3-3-3600-200000111-20000
χ22111111111111111111111iiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ2311111111111111111-1-1-1-1iiiiiiiiiiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii
χ241111111-111111-1-1-1-11-11-1iiiiiii−iiiiii−i−i−i−ii−ii−i-1-1-1-1-1-1-11-1-1-1-1-11111-11-11−i−i−i−i−i−i−ii−i−i−i−i−iiiii−ii−ii
χ251111111-111111-1-1-1-1-11-11iiiiiii−iiiiii−i−i−i−i−ii−ii-1-1-1-1-1-1-11-1-1-1-1-111111-11-1−i−i−i−i−i−i−ii−i−i−i−i−iiiiii−ii−i
χ26222222-102-1-1-1-10000020-12i2i2i2i2i2i−i02i−i−i−i−i000002i0−i-2-2-2-2-2-210-2111100000-201−2i−2i−2i−2i−2i−2ii0−2iiiii00000−2i0i
χ27222222-102-1-1-1-100000-2012i2i2i2i2i2i−i02i−i−i−i−i00000−2i0i-2-2-2-2-2-210-211110000020-1−2i−2i−2i−2i−2i−2ii0−2iiiii000002i0−i
χ2822222-120-12-1-1-1000020-102i2i2i2i2i−i2i0−i2i−i−i−i00002i0−i0-2-2-2-2-21-201-21110000-2010−2i−2i−2i−2i−2ii−2i0i−2iiii0000−2i0i0
χ2922222-120-12-1-1-10000-20102i2i2i2i2i−i2i0−i2i−i−i−i0000−2i0i0-2-2-2-2-21-201-2111000020-10−2i−2i−2i−2i−2ii−2i0i−2iiii00002i0−i0
χ3022-1-1-1222-1-12-1-12-1-1-100002i2i−i−i−i2i2i2i−i−i2i−i−i2i−i−i−i0000-2-2111-2-2-211-211-21110000−2i−2iiii−2i−2i−2iii−2iii−2iiii0000
χ3122-1-1-122-2-1-12-1-1-211100002i2i−i−i−i2i2i−2i−i−i2i−i−i−2iiii0000-2-2111-2-2211-2112-1-1-10000−2i−2iiii−2i−2i2iii−2iii2i−i−i−i0000
χ3244444-2-20-2-2111000000004i4i4i4i4i−2i−2i0−2i−2iiii00000000-4-4-4-4-422022-1-1-100000000−4i−4i−4i−4i−4i2i2i02i2i−i−i−i00000000
χ3344-2-2-24-20-21-211000000004i4i−2i−2i−2i4i−2i0−2ii−2iii00000000-4-4222-4202-12-1-100000000−4i−4i2i2i2i−4i2i02i−i2i−i−i00000000
χ3444-2-2-2-2401-2-211000000004i4i−2i−2i−2i−2i4i0i−2i−2iii00000000-4-42222-40-122-1-100000000−4i−4i2i2i2i2i−4i0−i2i2i−i−i00000000
χ3544-2-2-2-2-20111−1+3i32−1−3i32000000004i4i−2i−2i−2i−2i−2i0iii2ζ7−ζ11−ζ7+2ζ1100000000-4-4222220-1-1-11−3i321+3i3200000000−4i−4i2i2i2i2i2i0−i−i−i−2ζ7+ζ11ζ7−2ζ1100000000
χ3644-2-2-2-2-20111−1−3i32−1+3i32000000004i4i−2i−2i−2i−2i−2i0iii−ζ7+2ζ112ζ7−ζ1100000000-4-4222220-1-1-11+3i321−3i3200000000−4i−4i2i2i2i2i2i0−i−i−iζ7−2ζ11−2ζ7+ζ1100000000
χ376-36-3-300200000-12-1-100006i−3i6i−3i−3i002i00000−i2i−i−i0000-63-63300-2000001-2110000−6i3i−6i3i3i00−2i00000i−2iii0000
χ386-36-3-300-2000001-21100006i−3i6i−3i−3i00−2i00000i−2iii0000-63-63300200000-12-1-10000−6i3i−6i3i3i002i00000−i2i−i−i0000
χ396-3-36-300200000-1-12-100006i−3i−3i6i−3i002i00000−i−i2i−i0000-633-6300-20000011-210000−6i3i3i−6i3i00−2i00000ii−2ii0000
χ406-3-36-300-20000011-2100006i−3i−3i6i−3i00−2i00000ii−2ii0000-633-6300200000-1-12-10000−6i3i3i−6i3i002i00000−i−i2i−i0000
χ416-3-3-3600200000-1-1-1200006i−3i−3i−3i6i002i00000−i−i−i2i0000-6333-600-200000111-20000−6i3i3i3i−6i00−2i00000iii−2i0000
χ426-3-3-3600-200000111-200006i−3i−3i−3i6i00−2i00000iii−2i0000-6333-600200000-1-1-120000−6i3i3i3i−6i002i00000−i−i−i2i0000
χ43111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4411111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ451111111-111111-1-1-1-11-11-1-1-1-1-1-1-1-11-1-1-1-1-11111-11-111111111-111111-1-1-1-11-11-1-1-1-1-1-1-1-11-1-1-1-1-11111-11-11
χ461111111-111111-1-1-1-1-11-11-1-1-1-1-1-1-11-1-1-1-1-111111-11-11111111-111111-1-1-1-1-11-11-1-1-1-1-1-1-11-1-1-1-1-111111-11-1
χ47222222-102-1-1-1-10000020-1-2-2-2-2-2-210-2111100000-201222222-102-1-1-1-10000020-1-2-2-2-2-2-210-2111100000-201
χ48222222-102-1-1-1-100000-201-2-2-2-2-2-210-211110000020-1222222-102-1-1-1-100000-201-2-2-2-2-2-210-211110000020-1
χ4922222-120-12-1-1-1000020-10-2-2-2-2-21-201-21110000-201022222-120-12-1-1-1000020-10-2-2-2-2-21-201-21110000-2010
χ5022222-120-12-1-1-10000-2010-2-2-2-2-21-201-2111000020-1022222-120-12-1-1-10000-2010-2-2-2-2-21-201-2111000020-10
χ5122-1-1-1222-1-12-1-12-1-1-10000-2-2111-2-2-211-211-2111000022-1-1-1222-1-12-1-12-1-1-10000-2-2111-2-2-211-211-21110000
χ5222-1-1-122-2-1-12-1-1-21110000-2-2111-2-2211-2112-1-1-1000022-1-1-122-2-1-12-1-1-21110000-2-2111-2-2211-2112-1-1-10000
χ5344444-2-20-2-211100000000-4-4-4-4-422022-1-1-10000000044444-2-20-2-211100000000-4-4-4-4-422022-1-1-100000000
χ5444-2-2-24-20-21-21100000000-4-4222-4202-12-1-10000000044-2-2-24-20-21-21100000000-4-4222-4202-12-1-100000000
χ5544-2-2-2-2401-2-21100000000-4-42222-40-122-1-10000000044-2-2-2-2401-2-21100000000-4-42222-40-122-1-100000000
χ5644-2-2-2-2-20111−1+3i32−1−3i3200000000-4-4222220-1-1-11−3i321+3i320000000044-2-2-2-2-20111−1+3i32−1−3i3200000000-4-4222220-1-1-11−3i321+3i3200000000
χ5744-2-2-2-2-20111−1−3i32−1+3i3200000000-4-4222220-1-1-11+3i321−3i320000000044-2-2-2-2-20111−1−3i32−1+3i3200000000-4-4222220-1-1-11+3i321−3i3200000000
χ586-36-3-300200000-12-1-10000-63-63300-2000001-21100006-36-3-300200000-12-1-10000-63-63300-2000001-2110000
χ596-36-3-300-2000001-2110000-63-63300200000-12-1-100006-36-3-300-2000001-2110000-63-63300200000-12-1-10000
χ606-3-36-300200000-1-12-10000-633-6300-20000011-2100006-3-36-300200000-1-12-10000-633-6300-20000011-210000
χ616-3-36-300-20000011-210000-633-6300200000-1-12-100006-3-36-300-20000011-210000-633-6300200000-1-12-10000
χ626-3-3-3600200000-1-1-120000-6333-600-200000111-200006-3-3-3600200000-1-1-120000-6333-600-200000111-20000
χ636-3-3-3600-200000111-20000-6333-600200000-1-1-1200006-3-3-3600-200000111-20000-6333-600200000-1-1-120000
χ64111111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiii
χ6511111111111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiiiiiiiiiiii−i−i−i−i
χ661111111-111111-1-1-1-11-11-1−i−i−i−i−i−i−ii−i−i−i−i−iiiii−ii−ii-1-1-1-1-1-1-11-1-1-1-1-11111-11-11iiiiiii−iiiiii−i−i−i−ii−ii−i
χ671111111-111111-1-1-1-1-11-11−i−i−i−i−i−i−ii−i−i−i−i−iiiiii−ii−i-1-1-1-1-1-1-11-1-1-1-1-111111-11-1iiiiiii−iiiiii−i−i−i−i−ii−ii
χ68222222-102-1-1-1-10000020-1−2i−2i−2i−2i−2i−2ii0−2iiiii00000−2i0i-2-2-2-2-2-210-2111100000-2012i2i2i2i2i2i−i02i−i−i−i−i000002i0−i
χ69222222-102-1-1-1-100000-201−2i−2i−2i−2i−2i−2ii0−2iiiii000002i0−i-2-2-2-2-2-210-211110000020-12i2i2i2i2i2i−i02i−i−i−i−i00000−2i0i
χ7022222-120-12-1-1-1000020-10−2i−2i−2i−2i−2ii−2i0i−2iiii0000−2i0i0-2-2-2-2-21-201-21110000-20102i2i2i2i2i−i2i0−i2i−i−i−i00002i0−i0
χ7122222-120-12-1-1-10000-2010−2i−2i−2i−2i−2ii−2i0i−2iiii00002i0−i0-2-2-2-2-21-201-2111000020-102i2i2i2i2i−i2i0−i2i−i−i−i0000−2i0i0
χ7222-1-1-1222-1-12-1-12-1-1-10000−2i−2iiii−2i−2i−2iii−2iii−2iiii0000-2-2111-2-2-211-211-211100002i2i−i−i−i2i2i2i−i−i2i−i−i2i−i−i−i0000
χ7322-1-1-122-2-1-12-1-1-21110000−2i−2iiii−2i−2i2iii−2iii2i−i−i−i0000-2-2111-2-2211-2112-1-1-100002i2i−i−i−i2i2i−2i−i−i2i−i−i−2iiii0000
χ7444444-2-20-2-211100000000−4i−4i−4i−4i−4i2i2i02i2i−i−i−i00000000-4-4-4-4-422022-1-1-1000000004i4i4i4i4i−2i−2i0−2i−2iiii00000000
χ7544-2-2-24-20-21-21100000000−4i−4i2i2i2i−4i2i02i−i2i−i−i00000000-4-4222-4202-12-1-1000000004i4i−2i−2i−2i4i−2i0−2ii−2iii00000000
χ7644-2-2-2-2401-2-21100000000−4i−4i2i2i2i2i−4i0−i2i2i−i−i00000000-4-42222-40-122-1-1000000004i4i−2i−2i−2i−2i4i0i−2i−2iii00000000
χ7744-2-2-2-2-20111−1+3i32−1−3i3200000000−4i−4i2i2i2i2i2i0−i−i−i−2ζ7+ζ11ζ7−2ζ1100000000-4-4222220-1-1-11−3i321+3i32000000004i4i−2i−2i−2i−2i−2i0iii2ζ7−ζ11−ζ7+2ζ1100000000
χ7844-2-2-2-2-20111−1−3i32−1+3i3200000000−4i−4i2i2i2i2i2i0−i−i−iζ7−2ζ11−2ζ7+ζ1100000000-4-4222220-1-1-11+3i321−3i32000000004i4i−2i−2i−2i−2i−2i0iii−ζ7+2ζ112ζ7−ζ1100000000
χ796-36-3-300200000-12-1-10000−6i3i−6i3i3i00−2i00000i−2iii0000-63-63300-2000001-21100006i−3i6i−3i−3i002i00000−i2i−i−i0000
χ806-36-3-300-2000001-2110000−6i3i−6i3i3i002i00000−i2i−i−i0000-63-63300200000-12-1-100006i−3i6i−3i−3i00−2i00000i−2iii0000
χ816-3-36-300200000-1-12-10000−6i3i3i−6i3i00−2i00000ii−2ii0000-633-6300-20000011-2100006i−3i−3i6i−3i002i00000−i−i2i−i0000
χ826-3-36-300-20000011-210000−6i3i3i−6i3i002i00000−i−i2i−i0000-633-6300200000-1-12-100006i−3i−3i6i−3i00−2i00000ii−2ii0000
χ836-3-3-3600200000-1-1-120000−6i3i3i3i−6i00−2i00000iii−2i0000-6333-600-200000111-200006i−3i−3i−3i6i002i00000−i−i−i2i0000
χ846-3-3-3600-200000111-20000−6i3i3i3i−6i002i00000−i−i−i2i0000-6333-600200000-1-1-1200006i−3i−3i−3i6i00−2i00000iii−2i0000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.